THE PROCRUSTES CLASS OF FACTOR-ANALYTIC TRANSFORMATIONS.

Area of Science:

• Multivariate statistics
• Factor analysis

Background:

• Principal-axes factor analysis is a common technique for data reduction.
• Deriving a stable and interpretable reference structure is crucial for factor analysis.
• Existing transformation methods may lack a unified framework.

Purpose of the Study:

• To demonstrate that the Procrustes method represents a class of solutions for factor structure transformation.
• To unify various factor transformation techniques under the Procrustes framework.
• To clarify the differences in generating the target matrix H among methods.

Main Methods:

• The study frames the Procrustes method as a general approach to factor transformation.
• It analyzes how different methods (Promax, eigenvector rotation, classical Procrustes) generate a target matrix H.
• The core idea is to find a transformation matrix that minimizes the distance between the rotated factor matrix and H.

Main Results:

• The Procrustes method is shown to be a general class of solutions for rotating factor matrices.
• Various factor transformation techniques are demonstrated to be specific instances of this Procrustes framework.
• Differences among methods are primarily attributed to their distinct approaches in generating the target matrix H.

Conclusions:

• The Procrustes method provides a unifying perspective on factor transformation techniques.
• Understanding the generation of matrix H is key to differentiating these methods.
• This framework aids in selecting appropriate transformations for principal-axes factor matrices.